No sound when using separate speaker and microphone

I have a Bluetooth speaker and a USB microphone (Shure MV7) connected to my Windows 11 machine.

When using the Teams desktop application, I only hear sound when I have my speaker selected as both the microphone and speaker. If I switch the microphone setting to my USB microphone, the sound stops. I can also hear sound when I have my microphone selected as both the microphone and speaker - through its sound monitor output.

Setup 1 (Sound works): Speaker = Bluetooth speaker, Microphone = Bluetooth speaker

Setup 2 (Sound works): Speaker = USB mic, Microphone = USB microphone

Setup 3 (No sound): Speaker = Bluetooth speaker, Microphone = USB microphone

If I use the web version of Teams, everything works fine for all of those combinations.